Any idea how they insulated the tent?
They called it a "four-season" tent, and it had a stovepipe coming out the top. They didn't show the inside. Wood (presumably for the stove) was nearby. No mention was made of how the tent was insulated.
With a wood stove you don't actually need to insulate the tent - just add 10 minutes to the time it takes to get a roaring fire going inside that stove and it is unbeliveably hot in there.
I'm not against insulating the tent, and any insulation will greatly add to your comfort level. But there is little actuall need to do so.
Without insulation the temperature will drop like a brick when the stove goes out. But if you have proper sleeping arrangements that isn't a problem. For me, proper sleeping arrangements means a sleeping bag rated for the outside temperature plus a comfortable safe margin plus adjusting my layered clothing to fine tune so I'm comfortable. Don't know what "proper sleeping arrangements" means to those trappers, but I can take a guess of wool blankets, fur and the like.
If you can't sleep inside something warm enough for the outside temperature you will have to wake up every now and then to get the fire going again. Insulating the tent will keep you asleep longer, but probably not through the whole night. You can also use tricks like hot rocks or bottles of hot water to keep you warm. Disturbed sleep is better than freezing to death or no sleep at all.
And insulating will of course greatly reduce fuel consumption. Probably not your biggest concern when your shack has burned down, but it could be in the long run.